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If there is no time pressure, rerolling is probably OK. The penalty for failure in this case is that you spend extra time doing it. The more important question is "Was the roll even necessary?"
This actually brings us back to one of the key points in the advice for DM in the game manual. It looks like a throw away line, but it's a good guide for when to ...

Give bonus skill points for a good backstory!
If someone writes up a good backstory, and the character should logically have certain skills from that backstory, that aren’t actually useful (or, at least, unlikely to be useful) in the campaign, turn those skills into rewards for writing a good backstory.
That’s a great story of how a former ...

10 yes (sort of), 20 no.
Taking 20 was not a thing in 4th edition, and is similarly absent from 5th. Taking 10 however is sort of a thing in 5th, but it's not implemented the way you might think it should be.
Basically, the way "taking 10" works in 5e is that every ability (And by extension, skill), has a "passive" score (Basic Rules v2 page 59). This is ...

You can always use a skill you're untrained in, and you can use it in any way not marked as (Trained Only). Being trained means higher numbers, and unlocking the trained only applications of the skill.
Consider Athletics and Acrobatics: nobody needs training to be able to jump, climb, swim or balance. (At least, adventurers are assumed to be minimally ...

You have two good options here:
Roll for them
Don't have them take 10, as this gives them a statistically worse chance of succeeding than rolling. Also be sure you know exactly how much each character adds to Spot, Listen, Sense Motive, Search and whatever other checks you are handling this way. It is likely that characters who care about these rolls add ...

This is how skills are supposed to work!
If you are in a situation where there is only one person doing something, and they are rolling a single skill check, then yes, this is how it's supposed to work. Giving help is a natural thing and should be used in situations like this. There is no reason to prevent it unless the task is clearly something that's not ...

Passive Investigation could be a way to determine whether to feed players information that their character might pick up on, but the player might not think to explicitly ask. Note that a passive check can be against a DC, rather than an opposed roll. Some examples:
From the angle of the body, it looks like the Mayor didn't fall... She was pushed!
That ...

Aid Another is not broken...
That perception check example you give, its supposed to work that way 100 percent. Conceivably the players could also just stand in a room and continue to roll perception checks until they get a number they like. If the situation has no inherent danger punishing a failed skill roll should have no consequences.
A creature ...

Short Answer: No
It definitely does not count as ranks; it is a bonus. It’s effectively equivalent to the Skill Focus feat (which also provides an untyped permanent bonus). It does stack with Skill Focus, though, since they are different (and also does not count as Skill Focus for requirements, though I recommend houseruling that one).
Relevant ...

The word include indicates a subset: every element that is included appears in the including set.
So the statement about the cloistered cleric’s class skills is that the given list, “Decipher Script, Speak Language, and all Knowledge skills (from the Knowledge domain, see below),” is a subset of the full set cloistered cleric class skills. ...

There are a few classes you can multiclass into to gain skills, such as Bard, Ranger or Rogue.
In addition to that, in the player's handbook there is a feat called "Skilled" which allows you to gain proficiency in any combination of 3 skills or tools.
There is also a bard ability in the college of lore that allows you to learn 3 more skills at level 3.
...

It goes negative
This is a case of "the rules don't say otherwise". In particular, the Skills section has nothing to say about results being "low-capped" at 0.
Skills can be further modified by a wide variety of sources—by your race, by a class ability, by equipment, by spell effects or magic items, and so on. [...]
If the result of your skill ...

Stunts
I would argue that this falls perfectly under the application of stunts - using one skill in place of another. From Your Story p.147:
The first possible use for a stunt is to broaden a skill by giving it a new trapping. Often this is a trapping that’s “transplanted” from one skill to another. Sometimes this trapping may need to be modified, or ...

A +29 on Intimidate is a very large bonus. Especially on a fighter, who has few skill points and little use for Charisma in most cases; almost all of that is probably from skill ranks, which implies a very high level character.
Such a person should be trivially succeeding on attempts to demoralize most anything. Anything short of an actual god should be an ...

From http://www.d20pfsrd.com/skills/fly
You generally need only make a Fly check when you are attempting a complex maneuver. Without making a check, a flying creature can remain flying at the end of its turn so long as it moves a distance greater than half its speed. It can also turn up to 45 degrees by sacrificing 5 feet of movement, can rise at half ...

Profession(Cook, butcher or similar) or survival would be useful to identify the normal kinds of wild meat game (for survival) or the most usual types of meat used in cooking (for the professions), or to determine that a certain kind of meat is not one of the usual types, but not necesarily be able to identify it.
Honestly, unless the characters had ...

As you state correctly, a character can have a maximum number of skill ranks in any skill equal to its Hit Dice.
Hit Die, singular, (i.e. the bards d8) is a basic component of a class and only determines the amount of hit points a character gets upon taking a level in the class1. It is (hopefully) never abbreviated HD.
Hit Dice (or HD), plural, means the ...

Diplomacy have a built-in limit:
You cannot use Diplomacy against a creature that does not understand you or has an Intelligence of 3 or less.
So, you can use it on Ooze, Brain - it has Int, telepathy 100ft and language. But it is exceptional ooze, no longer mindless.
For Plants, you can try Awaken them, and then use this skill as normal.
Certain ...

Would players be tempted to do something out of character that might spoil the game for fomeone? If not, let them roll. Are you (almost) sure they will resist the temptation? Let them roll. Rolling is fun, so unless a roll spoils some bigger fun, let the players roll.
Most of my passive perception rolls (different system, but shouldn't matter) are done by ...

The DM can always make house rules...
If the DM wants no dancing cats in his campaign, the DM can rule that cats can't put skill ranks into the skill Perform (dance) and cruelly further rule that cats always fail Perform (dance) skill checks. Such a campaign is a much sadder place for such a house rule, but there it is.
...But some creatures can't put ...

If no restriction is listed (and I can confirm that none is), no restriction exists. It’s related to psionics because the only classes that have it in-class are psionic classes, but others can use it just fine. As you say, there’s no reason it should be restricted, and lo and behold, it’s not.

Exploration is generally handled in a much more free-form manner
In some games, the shift from exploration or other non-combat conflicts to combat is barely noticeable. But 4e has very strict rules for its combat, that's the game's strongest point. In a way, 4e combat is its own separate game which gets initiated from time to time.
When not in combat, ...

Skill Point Cost: Only current class’s class skills
From Skills Summary
Each skill point you spend on a cross-class skill gets your character ½ rank in that skill. Cross-class skills are skills not found on your character’s class skill list.
From Player’s Handbook pg. 60.
Skill points must be spent according to the class that the ...

You cannot learn spells of another class without actually multi-classing or picking up a feat like Ritual Caster or Magic Initiate.
While there is some overlap in class spell lists you can only ever learn the spells of your class unless you make the choice to multi-class or forgo the stat increase to pickup one of the two feats I noted above.
Proficiency ...

Perception seems to fit the bill. It's a DC 5 check to determine whether food you're about to eat is spoiled; at higher DCs, one should be able to tell whether the meat they're eating is actually pig or lamb or…something else less salubrious. Plus, it's tied to Wisdom and the senses, both of which would be in use here.

Whenever a PC makes what 5e calls an Ability Check, such as Dexterity(Stealth), they roll a d20, add their Ability Score Modifier, and their Proficiency Bonus if they are proficient with that skill. A PC Proficient in Stealth would add their Dexterity Modifier as well as their Proficiency Bonus.
This information is in Chapter 7: Using Ability Scores. It ...

An Intelligence check is appropriate for this task. According to page 178 of the PHB, an Intelligence check can be used for a number of things, including:
Estimate the value of a precious item
As far as what skill can be used on this check, or whether a skill can be used at all, I leave it up to my players to suggest a skill that might apply and ...

Rules for group checks in DnD 5e can be found on page 59 of the player's basic rules or page 175 of the PHB and are as follows:
To make a group ability check, everyone in the group makes the ability check. If at least half the group succeeds, the whole group succeeds. Otherwise, the group fails.

Don't
You use the guns skill to use guns, its just that simple. Sounds like your friend/player is trying to get you to houserule something to make his character more powerful. Even using an aspect to do this would be too powerful and potentially game breaking.
Discipline the skill does not mean trigger-discipline. Its a representation of your character's ...